Method for modeling a compressor speed

ABSTRACT

A method is provided for modeling the compressor speed of a turbocharger, and includes determining the temperature difference across the compressor, determining the mass flow through the compressor, and calculating a compressor speed value as a function of the temperature difference across the compressor and the mass flow.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. application Ser. No.15/561,035, filed Sep. 23, 2017, which claims priority to 371International Application No. PCT/EP2015/059909, filed May 6, 2015,which is incorporated herein by reference.

BACKGROUND AND SUMMARY

The invention relates to a method for modeling the speed of acompressor, in particular for a turbocharger.

The invention can be applied in heavy-duty vehicles, such as trucks,buses and construction equipment. Although the invention will bedescribed with respect to a truck, the invention is not restricted tothis particular vehicle, but may also be used in other applicationsutilizing turbocharger units such as aero or marine systems.

A turbocharger is a vehicle component used together with an associatedinternal combustion engine, typically a diesel engine. The turbochargeris configured to recover a part of the energy of the exhaust gas and touse that energy to compress intake air flowing into the combustionchamber of the internal combustion engine. Turbochargers are commonlyprovided for increasing the efficiency and power of the internalcombustion engine.

A turbocharger has three main components; a turbine for convertingenergy of the exhaust gas flow to a rotational movement of the turbine,a compressor rotationally connected to the turbine for compressingintake air, and a housing enclosing the turbine and the compressor aswell as a rotating shaft, bearings, etc.

In order to monitor the wear of the rotating parts of the turbochargerit is desirable to determine the speed of the turbine or the compressor.In particular, wear of the compressor is typically categorized by lowcycle fatigue and high cycle fatigue. Low cycle fatigue corresponds torelatively small fluctuations in compressor speed, while high cyclefatigue corresponds to relatively rapid (and large) changes incompressor speed. Fatigue will eventually lead to substantial changes inthe material structure of the compressor, which may lead to a suddenbreakage of the compressor. Such breakage will in most cases lead to amalfunction of the entire turbocharger, requiring standstill of thevehicle and costly service and/or replacement of the turbocharger.

Different solutions for monitoring the compressor speed have beenproposed. In particular, it has been suggested to arrange a physicalspeed sensor at the compressor. However, more recent solutions have beensuggested in which the physical sensor is replaced by a compressor speedmodel for estimating the compressor speed.

One solution for modeling the speed of a double-stage turbocharger isdescribed in US2009/0314082. Here, the speed of each turbine is modeledseparately and the temperature as well as the pressure between theturbines is used as input for the speed estimation, as well as anambient pressure value. While US2009/0314082 requires a number ofphysical sensors for providing the necessary input data, it would beadvantageous to provide a speed modeling method reducing this number ofrequired sensors.

It is desirable to provide a method for modeling the compressor speedovercoming the above mentioned drawbacks of prior art methods.

By determining the temperature difference across the compressor, and usethis temperature difference as input for the compressor speed model, itis no longer necessary to have an ambient pressure sensor providinginput data for the model.

A method for modeling the compressor speed of a turbocharger istherefore provided, comprising i) determining the temperature differenceacross the compressor, ii) determining the mass flow through thecompressor, and iii) calculating a compressor speed value as a functionof the temperature difference across the compressor and the mass flow.

In an embodiment, the step of calculating the compressor speed value isperformed using

${N_{turbo} \propto {\frac{d\; m_{gas}}{dt}{\overset{\sim}{R}\left( {T_{boost} - T_{i\; n}} \right)}}},$where N_(turbo) is the compressor speed,

$\frac{d\; m_{gas}}{dt}$is the mass flow, {tilde over (R)} is a corrected ideal gas constant,and T_(boost)−T_(in) is the temperature difference across thecompressor. This thermodynamic approach does not require the pressureratio across the compressor, thus leading to significant reduction inhardware complexity of the associated turbocharger.

In an embodiment,

$N_{turbo} \propto {\frac{d\; m_{gas}}{dt}{\overset{\sim}{R}\left( {T_{boost} - T_{i\; n}} \right)}}$is calculated using

$N_{turbo} = {{F\left( {\frac{d\; m_{gas}}{dt},{T_{boost} - T_{i\; n}}} \right)}.}$Reducing the relationship in this manner greatly facilitates thenecessary computing for modeling the compressor speed.

In an embodiment the step of calculating the compressor speed value isperformed by a polynomial representation of

$N_{turbo} = {F\left( {\frac{d\; m_{gas}}{dt},{T_{boost} - T_{i\; n}}} \right)}$according to:

${F\left( {\frac{d\; m_{gas}}{dt},{T_{boost} - T_{i\; n}}} \right)} = {{F\left( {x,y} \right)} = {{a_{1}x^{2}} + {a_{2}{xy}} + {a_{3}y^{2}} + {a_{4}x} + {a_{5}y} + {a_{6}.}}}$This has proven to provide a good fit for the relationship.

In an embodiment, the method further comprises the step of determiningif a recovered exhaust gas flow is introduced downstream the compressor.Further the step of determining the mass flow is performed bydetermining the mass flow of the gas exiting the compressor andcorrecting the determined mass flow by a factor corresponding torecovered exhaust gas flow. By introducing the effects caused byrecovered exhaust gas flow, the accuracy of the modeling method isimproved.

In an embodiment the step of determining the temperature differenceacross the compressor is performed by estimating the temperaturedownstream the compressor, and by subtracting the estimated temperaturefrom a measured ambient temperature. Since it is difficult to arrange aphysical temperature sensor close to the compressor, an estimatedtemperature just downstream the compressor will provide a more accuratevalue for the resulting temperature difference.

In an embodiment the step of estimating the temperature downstream thecompressor is performed by measuring the temperature in an air inletmanifold, and correcting this temperature by a factor corresponding tothe temperature loss across an associated cooler. Hence, accuracy of thespeed modeling method is further improved.

In an embodiment the method further comprises the step of determiningthe pressure ratio across the compressor. Further, the step ofcalculating the compressor speed value is performed by calculating thecompressor speed value as a function of the pressure ratio. By includingthe pressure ratio across the compressor as input for the compressorspeed modeling method, accuracy may be further improved.

In an embodiment the step of determining the pressure ratio across thecompressor is performed by determining if the ambient pressure is belowa preset ambient pressure corresponding to high altitude conditions, andif so, setting the ambient pressure as the preset ambient pressure, anddividing the boost pressure with the ambient pressure. In thisembodiment, high altitude conditions are also considered. This is highlybeneficial for increasing the accuracy of the speed modeling. As thereis otherwise a risk of overestimating the compressor speed, this willavoid unnecessary torque derate at higher altitudes as well as wrongcalculations for low cycle fatigue.

In an embodiment the step of calculating the compressor speed value isperformed by estimating a compressor speed value using the pressureratio as input, and calculating a corrected compressor speed value fromthe estimated compressor speed value and the actual ambient pressure.This has proven to provide an accurate model performance.

According to a second aspect, a method for modeling the compressor speedof a turbocharger is also provided. The method comprises i) determiningthe ambient pressure, ii) determining if the ambient pressure is below apreset ambient pressure corresponding to high altitude conditions, andif so, setting the ambient pressure as the preset ambient pressure, iii)determining a pressure ratio from the boost pressure and the ambientpressure, iv) estimating a compressor speed value using the pressureratio as input, and v) calculating a corrected compressor speed valuefrom the estimated compressor speed value and the actual ambientpressure. Similar to what has been discussed above, this is highlybeneficial for increasing the accuracy of the speed modeling. As thereis otherwise a risk of overestimating the compressor speed, this willavoid unnecessary torque derate at higher altitudes as well as wrongcalculations for low cycle fatigue.

In an embodiment the method comprises the further steps of determiningthe temperature difference across the compressor, determining the massflow through the compressor, and calculating a compressor speed value asa function of the pressure ratio, the temperature difference across thecompressor, and the mass flow.

In an embodiment, the step of calculating the compressor speed value isperformed by a polynomial representation of

${N_{turbo} = {{F\left( {\frac{d\; m_{gas}}{dt},{T_{boost} - T_{i\; n}},P_{ratio}} \right)} = {{F\left( {x,y,z} \right)} = {{a_{1}x^{2}} + {a_{2}{xy}} + {a_{3}y^{2}} + {a_{4}x} + {a_{5}y} + {a_{6}z^{2}} + {a_{7}z} + a_{8}}}}},$where N_(turbo) is the compressor speed,

$\frac{d\; m_{gas}}{dt}$is the mass flow, T_(boost)−T_(in) is the temperature difference acrossthe compressor, and P_(ratio) is the pressure ratio across thecompressor.

In an embodiment, the method comprises the further step of determiningif a recovered exhaust gas flow is introduced downstream the compressor,and wherein the step of determining the mass flow is performed bydetermining the mass flow of the gas exiting the compressor andcorrecting the determined mass flow by a factor corresponding torecovered exhaust gas flow.

In an embodiment the step of determining the temperature differenceacross the compressor is performed by estimating the temperaturedownstream the compressor, and by subtracting the estimated temperaturefrom a measured ambient temperature.

In an embodiment the step of estimating the temperature downstream thecompressor is performed by measuring the temperature in an air inletmanifold, and correcting this temperature by a factor corresponding tothe temperature loss across an associated cooler.

A computer program is also provided, comprising program code means forperforming the steps of any of the aspects above when said program isrun on a computer.

A computer readable medium is also provided, carrying a computer programcomprising program code means for performing the steps of any of theabove mentioned aspects when said program product is run on a computer.

A controller for modeling the compressor speed of a turbocharger is alsoprovided. The controller is configured to perform the steps of themethod according to the first and second aspects described above.

A controller for modeling the compressor speed of a turbocharger is alsoprovided. The controller comprises a processor and a memory, said memorycontaining instructions executable by the processor. The controller isoperative to determining the temperature difference across thecompressor, determining the mass flow through the compressor, andcalculating a compressor speed value as a function of the temperaturedifference across the compressor and the mass flow.

In an embodiment the controller is further operative to perform themethod according to the first or second aspects described above.

A controller for modeling the compressor speed of a turbocharger is alsoprovided. The controller comprises a processor and a memory, said memorycontaining instructions executable by the processor. The controller isoperative to determining the ambient pressure, determining if theambient pressure is below a preset ambient pressure corresponding tohigh altitude conditions, and if so, setting the ambient pressure as thepreset ambient pressure, determining a pressure ratio from the boostpressure and the ambient pressure, estimating a compressor speed valueusing the pressure ratio as input, and calculating a correctedcompressor speed value from the estimated compressor speed value and theactual ambient pressure.

In an embodiment the controller is further operative to perform themethod according to the second aspect described above.

A controller for modeling the compressor speed of a turbocharger is alsoprovided. The controller comprises a first module configured todetermining the temperature difference across the compressor, a secondmodule configured to determining the mass flow through the compressor,and a third module configured to calculating a compressor speed value asa function of the temperature difference across the compressor and themass flow.

In an embodiment the controller further comprises additional modulesconfigured to perform the method according to the first aspect describedabove.

A controller for modeling the compressor speed of a turbocharger is alsoprovided. The controller comprises a first module configured todetermining the ambient pressure, a second module configured todetermining if the ambient pressure is below a preset ambient pressurecorresponding to high altitude conditions, and if so, setting theambient pressure as the preset ambient pressure, a third moduleconfigured to determining a pressure ratio from the boost pressure andthe ambient pressure, a fourth module configured to estimating acompressor speed value using the pressure ratio as input, and a fifthmodule configured to calculating a corrected compressor speed value fromthe estimated compressor speed value and the actual ambient pressure.

In an embodiment the controller further comprises additional modulesconfigured to perform the method according to the second aspectdescribed above.

A vehicle is also provided, comprising a controller according to theaspects described above.

BRIEF DESCRIPTION OF THE DRAWINGS

With reference to the appended drawings, below follows a more detaileddescription of embodiments of the invention cited as examples.

In the drawings:

FIG. 1 is a side view of a vehicle according to an embodiment,

FIG. 2 is a schematic view of an internal combustion engine according toan embodiment,

FIG. 3 is a schematic view of a controller according to an embodiment,

FIG. 4 is a schematic view of a controller according to an embodiment,

FIG. 5 is a diagram showing the engine speed as a function of enginetorque for a vehicle according to an embodiment, and

FIGS. 6 and 7 are schematic views of methods according to differentembodiments.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS OF THE INVENTION

Starting with FIG. 1 a vehicle 10 is shown. The vehicle 10, which isillustrated as a truck, has an internal combustion engine 100 fordriving the vehicle 10. As will be further explained below the internalcombustion engine 100 of the vehicle 10 is provided with a turbocharger130 and a controller 200. The vehicle 10 may have additional propulsionunits, such as electric drives etc. as long as it has at least oneengine providing a flow of exhaust gases interacting with theturbocharger unit 130. Hence the vehicle 10 is not exclusively a truckbut may also represent various vehicles such as buses, constructionalequipment, etc.

In FIG. 2 an example of an internal combustion engine 100 is shown. Theinternal combustion engine 100 includes a cylinder block 102 beingprovided with a plurality of cylinders 104 operated to combust fuel,such as diesel or gasoline, whereby the motion of pistons reciprocatingin the cylinders 104 is transmitted to a rotation movement of a crankshaft 156. The crank shaft 110 is further coupled to a transmission (notshown) for providing a torque to driving elements (not shown). In caseof a heavy vehicle, such as a truck, the driving elements are wheels;however the internal combustion engine 100 may also be used for otherequipment such as construction equipment, marine applications, etc.

The internal combustion engine 100 further comprises an exhaust gassystem 120, which system 120 serves the purpose of recovering at leastsome of the energy in the exhaust gas flow to improve the performance ofthe internal combustion engine 100. In the shown example the exhaust gasexits the cylinders 104 and enters an exhaust manifold 106 which isfurther connected to an exhaust inlet 132 of a turbocharger unit 130.The exhaust gas flow causes a turbine 134 arranged inside a turbinehousing to rotate, which rotation is translated via a shaft 135 to acorresponding rotation of a compressor 136 arranged inside a compressorhousing and being used to compress incoming air before it is introducedin the cylinders 104.

Air is introduced to interact with the compressor 136 via an air inlet140. Downstream the compressor 136, i.e. after the incoming air iscompressed, it is guided by an air conduit 142 to an air inlet manifold144 being connected with the cylinders 104. A cooler 146, such as acharged air cooler, may be provided in the air conduit 142.

Some of the exhaust gas flow may be re-circulated to the cylinders 104via the air conduit 142 in order to provide exhaust gas recovery. Forthis a bypass line 108 may at one end be connected to the exhaust gasflow path at a position between the exhaust gas manifold 106 and theexhaust gas inlet 132 of the turbocharger 130. A second end of thebypass line 108 is connected to the air conduit 142 somewhere downstreamthe compressor 136.

A controller 200 is also provided for modeling the speed of thecompressor 136. The controller 200 comprises a processor 202 and amemory 204, wherein the memory 204 contains instructions executable bythe processor 202.

The memory 204 may be implemented by any known memory technology,including but not limited to E(E)PROM, S(D)RAM and flash memory, and itmay also include secondary storage such as a magnetic or optical disc.Physically, the memory 204 may consist of or comprise one unit or aplurality of units which together constitute the memory 204 on a logicallevel. In some embodiments, it may be implemented at least partly by astorage area in another component of the controller 200. The processor202 is overall responsible for the operation of the controller 200. Theprocessor 202 may e.g. be implemented by means of a PLC, CPU, and/or DSPcapable of performing the intended functionality.

The controller 200 is operative to receive a plurality of data inputs,and to model the compressor speed as a function of at least some of thedata inputs. For this, a number of sensors 150 a-e are provided andconfigured to measure various parameters of the air flowing into, andout from, the compressor 136. The sensors 150 a-e are connected to thecontroller 200. In one embodiment, a temperature sensor 150 a isarranged in the air inlet manifold 144 for providing data correspondingto the boost temperature T_(boost). A pressure sensor 150 b may bearranged in the air inlet manifold 144 for providing data correspondingto the boost pressure P_(boost). A further sensor 150 c may be arrangedin the air conduit 142 immediately downstream the compressor 136 forproviding data corresponding to the mass air flow

$\frac{{dm}_{gas}}{dt}.$Additional sensors 150 d-e may be provided in the air conduit 142upstream the compressor 136 for providing data corresponding to theambient temperature T_(in) and the ambient pressure p_(amb).

According to one specific aspect, the sensors 150 a, 150 d, and 150 care used for allowing the controller to determine the speed of thecompressor 136. According to this particular aspect, as is shown in FIG.3, the controller 200 includes a number of modules 210, 212, 214, 216.The modules 210, 212, 214, 216 may be implemented by hardware and/orsoftware. A first module 210 is configured to determine the temperaturedifference across the compressor 136 from the boost temperature and theinlet, or ambient temperature. Hence, the controller 200 receivesmeasured sensor data from the sensors 150 a, 150 d. The second module212 is configured to determine the mass flow. Hence, the controller 200receives measured sensor data from the sensor 150 c. The third module214 is configured to calculate the compressor speed N_(turbo) from thedetermined temperature difference and the determined mass flow. A fourthmodule 216 is also provided and configured to communicate the modeledcompressor speed to an associated unit for monitoring the current statusof the turbocharger components, especially in terms of service andmaintenance. The associated unit may either be arranged on-board thevehicle, or remote from the vehicle.

The third module 214 is preferably calculating the compressor speedvalue using a relationship in the form of

${N_{turbo} \propto {\frac{{dm}_{gas}}{dt}{\overset{\sim}{R}\left( {T_{boost} - T_{in}} \right)}}},$where N_(turbo) is the compressor speed,

$\frac{{dm}_{gas}}{dt}$is the mass flow, {tilde over (R)} is a corrected ideal gas constant,and T_(boost)−T_(in) is the temperature difference across thecompressor. The relationship of

$N_{turbo} \propto {\frac{{dm}_{gas}}{dt}{\overset{\sim}{R}\left( {T_{boost} - T_{in}} \right)}}$may preferably be calculated using

${N_{turbo} = {F\left( {\frac{{dm}_{gas}}{dt},{T_{boost} - T_{in}}} \right)}},$as will be further described below.

Calculating the compressor speed value may be performed by forming apolynomial representation of

$N_{turbo} = {F\left( {\frac{{dm}_{gas}}{dt},{T_{boost} - T_{in}}} \right)}$according to

${F\left( {\frac{{dm}_{gas}}{dt},{T_{boost} - T_{in}}} \right)} = {{F\left( {x,y} \right)} = {{a_{1}x^{2}} + {a_{2}{xy}} + {a_{3}y^{2}} + {a_{4}x} + {a_{5}y} + {a_{6}.}}}$

In general, the following relationship between turbo power and gasproperty before and after the compressor is assumed to be valid:

${{\overset{.}{W}}_{supplied} \propto {{p_{boost}\frac{{dV}_{out}}{dt}} - {p_{amb}\frac{{dV}_{in}}{dt}}}} = {\frac{{dm}_{gas}}{dt}{\overset{\sim}{R}\left( {T_{boost} - T_{in}} \right)}}$

As is evident, the mass flow relationship is much simpler than anequivalent volume velocity relationship. Hence, only the mass flowrelationship is used in the modeling procedure as presented herein. Thepower supply needed to maintain a certain level of mass flow at a giventemperature increase will also be proportional to the turbo speed,N_(turbo) according to {dot over (W)}_(supplied)∝N_(turbo). Thus,

${N_{turbo} \propto {{p_{boost}\frac{{dV}_{out}}{dt}} - {p_{amb}\frac{{dV}_{in}}{dt}}}} = {\frac{{dm}_{gas}}{dt}{\overset{\sim}{R}\left( {T_{boost} - T_{in}} \right)}}$applies. The mass flow may either be measured, or calculated by applyingthe following equation:ρ_(gas after compressor) =p _(boost)/({tilde over (R)} _(gas) T_(boost))

The gas specific ideal gas law constant is calculated as {tilde over(R)}_(gas)=R /M_(gas), while the molar mass of the gas is dependent on λand exhaust gas recovery fraction, β:

  M_(gas) = M_(air)(1 − β) + M_(EGR)β$M_{EGR} = {\frac{1}{a + \frac{b}{2} + {\left( {\lambda - 1} \right)\left( {a + \frac{b}{4}} \right)} + {3.773{\lambda\left( {a + \frac{b}{4}} \right)}}}{\left( {{aM}_{{CO}_{2}} + {\frac{b}{2}M_{H_{2}O}} + {\left( {\lambda - 1} \right)\left( {a + \frac{b}{4}} \right)M_{O_{2}}} + {3.773{\lambda\left( {a + \frac{b}{4}} \right)}M_{N_{2}}}} \right).}}$

The parameters, a and b, may be given by a fuel model structure. Acommon model of diesel which may be used is iso-octane, C₈H₁₈.

The ideal mass flow may thus be calculated, for a four-stroke dieselengine of size V_(engine) and engine speed N_(engine), as:

$\frac{{dm}_{gas}}{dt} = {\frac{1}{2}V_{engine}N_{engine}{\rho_{{gas}\mspace{14mu}{after}\mspace{11mu}{compressor}}.}}$

In a real application, the ideal mass flow above may not be a realisticquantity. For providing a better estimation, the volumetric efficiencycould also be considered. A simple model of the volumetric efficiency is

$\mu_{vol} = {{f\left( {N_{engine},\frac{p_{exhaust}}{p_{boost}}} \right)}.}$For reasons of simplicity, a decomposition of the engine speed andpressure dependency may preferably be made according to (c_(r):compression ratio):

$\mu_{vol} = {{g\left( N_{engine} \right)}{h\left( \frac{p_{exhaust}}{p_{boost}} \right)}}$${h\left( \frac{p_{exhaust}}{p_{boost}} \right)} = {\frac{c_{r}}{c_{r} - 1} - {\left( \frac{p_{exhaust}}{p_{boost}} \right)^{\frac{1}{\gamma}}\frac{1}{c_{r} - 1}}}$

The engine speed dependency, g(N_(engine)), may be semi-empiricallyderived (linearized).

Following the conclusion derived by from the equations above, a simpleassumption would be:

$N_{turbo} = {{F\left( {\frac{{dm}_{gas}}{dt},{T_{boost} - T_{in}}} \right)}.}$

The coefficients are preferably derived by application of a leastsquares criterion

$\frac{\partial{{erf}\left( \overset{\_}{\alpha} \right)}}{\partial\overset{\_}{\alpha}} = {{{- 2}{A^{T}\left( {z_{turbospeed} - {A\overset{\_}{\alpha}}} \right)}} = {\overset{\_}{0}.}}$The pseudo-inverse may thereafter be applied and the coefficients α arethen given as α=(A^(T)A)⁻¹A^(T)z_(turbospeed).

A good fit may be achieved for the function having the form

${F\left( {\frac{{dm}_{gas}}{dt},{T_{boost} - T_{in}}} \right)} = {{F\left( {x,y} \right)} = {{a_{1}x^{2}} + {a_{2}{xy}} + {a_{3}y^{2}} + {a_{4}x} + {a_{5}y} + {a_{6}.}}}$

As is realized

$\frac{{dm}_{gas}}{dt}$will not only be gas exiting the compressor, but also exhaust gasrecovery (EGR). However, if the EGR fraction, β (or equivalently, theEGR mass flow) is known the relationship may be formulated as

${F\left( {{\left( {1 - \beta} \right)\frac{{dm}_{gas}}{dt}},{T_{boost} - T_{in}}} \right)} = {{F\left( {x,y} \right)} = {{a_{1}x^{2}} + {a_{2}{xy}} + {a_{3}y^{2}} + {a_{4}x} + {a_{5}y} + {a_{6}.}}}$

The controller 200 may thus include a further module configured todetermine if a recovered exhaust gas flow is introduced downstream thecompressor. The module 212 for determining the mass flow may thus beconfigured to determine the mass flow of the gas exiting the compressorand correcting the determined mass flow by a factor corresponding torecovered exhaust gas flow.

The module 210 may in some embodiments be configured to determine thetemperature difference across the compressor by estimating thetemperature downstream the compressor, and by subtracting the estimatedtemperature from a measured ambient temperature.

For the controller shown in FIG. 3, additional modules may be providedfor including the impact of the pressure ratio across the compressor.Hence,

${F\left( {{\left( {1 - \beta} \right)\frac{{dm}_{gas}}{dt}},{T_{boost} - T_{in}},P_{ratio}} \right)} = {{F\left( {x,y,z} \right)} = {{a_{1}x^{2}} + {a_{2}{xy}} + {a_{3}y^{2}} + {a_{4}x} + {a_{5}y} + {a_{6}z^{2}} + {a_{7}z} + a_{8}}}$applies.

The temperature difference, T_(boost)−T_(in), can be used by itself. Asdescribed above, an even better approach may be to model the temperaturejust after the compressor. In order to do this the impact of EGR (with agiven temperature T_(EGR) and a given mass flow dm_(EGR)/dt should betaken into account.

The signal T_(boost) can then be used to model the temperature after thecharged air cooler 146 as

${T_{CAC} = {\left( \frac{1}{\frac{{dm}_{air}}{dt}} \right)\left( {{{k_{calibration}\left( {\frac{{dm}_{EGR}}{dt} + \frac{{dm}_{air}}{dt}} \right)}T_{boost}} - {T_{EGR}\frac{m_{EGR}}{dt}}} \right)}},{{where}\mspace{14mu} T_{EGR}\mspace{11mu}{and}\mspace{14mu}\frac{m_{EGR}}{dt}}$is either measured or estimated in the EMS. In order to retrieve thetemperature of the gas leaving the compressor, T_(compressor), thetemperature loss in the charger air cooler 146 could be accounted for.This may be done by using a map/function/model, f, that describes thetemperature drop in the charger air cooler as

${dT}_{CAC} = {{f\left( {\frac{{dm}_{air}}{dt},T_{compressor}} \right)}.}$

In such case there may be yet another expression for T_(CAC), namely

$T_{CAC} = {{T_{compressor} - {dT}_{CAC}} = {T_{compressor} - {{f\left( {\frac{{dm}_{air}}{dt},T_{compressor}} \right)}.}}}$

As the T_(CAC) is already known from the calculation after the chargerair cooler, it is possible to determine a unique value T_(compressor)for a given

$\frac{{dm}_{air}}{dt}.$

According to another aspect a controller 200 is provided for modelingthe compressor speed. The controller 200 is shown in FIG. 4, andcomprises a number of modules 220-230. A first module 220 is configuredto store a reference value for the ambient pressure, corresponding to ahigh altitude condition. Such preset ambient pressure may e.g. be 97kPa. A second module 222 is configured to determine if a measuredambient pressure, preferably being received by the sensor 150 e of FIG.2, is below the preset ambient pressure provided by module 220 andcorresponding to high altitude conditions. If so, the third module 224is configured to set the ambient pressure as the preset ambientpressure, and dividing the boost pressure with the ambient pressure toform a pressure ratio across the compressor 136. Hence, the pressureratio is set according to

$p_{ratio} = {\frac{p_{boost}}{\max\left( {p_{{amd},{present}},p_{{amb},{measure}}} \right)}.}$The fourth module 226 is configured to calculate the compressor speedvalue by estimating a compressor speed value using the pressure ratio asinput, and a fifth module 228 is configured to calculate a correctedcompressor speed value from the estimated compressor speed value and theactual ambient pressure. A sixth module 230 may be provided forcommunicating the modeled compressor speed communicate the modeledcompressor speed to an associated unit for monitoring the current statusof the turbocharger components, especially in terms of service andmaintenance. The associated unit may either be arranged on-board thevehicle, or remote from the vehicle.

The real measured ambient pressure p_(amb) may consequently be used inthe last step, when an estimated turbo speed N_(Turbo) has been modeled,according to N*_(Turbo)=p_(amb,measured)*N_(Turbo). This gives extremelygood model performance which can fulfil the accuracy requirementsdefined by either cost aspects or engine performance (removingunnecessary torque derate at high altitudes).

This aspect may preferably be combined with the first mentioned aspectdescribing the use of the temperature difference with respect to FIG. 3.By such combination, an improved model for the compressor speed isachieved. However, the aspect may also be combined with other compressorspeed models using the ambient pressure as input.

Now turning to FIG. 5, calibration of the model will be described. Thecalibration procedure may be performed straightforward as is suggestedby the equations above. A proper test cycle may preferably be provided,which test cycle is used to calibrate against. Therefore, it isadvantageous not to have a repetitive cycle that can shift thecalibration unfavorably towards one end due to reoccurring conditionsduring the cycle. A way to calibrate the model is therefore to generaterandom test-cycles with altering engine speeds and torques according tothe diagram shown in FIG. 5. Even more preferably, the test cyclesshould be representative for normal driving cycles. The speed/torquecombination should preferably fulfill the maximum torque dependency onengine speed. The value provided by the estimator can then be used foron-board diagnosis in order to monitor the rotating parts of theturbocharger and to create an information bank containing the current‘wear’ status of the said parts.

A suggested approach to calibrate the polynomial for the compressorspeed model is given by the diagram in FIG. 5. An engine speed-torquemesh may be created where a random walk is applied between given pointsin order to give unbiased and extensive data for model calibration.

In FIG. 6 a method 300 for modeling the speed of a compressor of aturbocharger is schematically shown. The method comprises a first step302 of determining the temperature difference across the compressor, anda second step 304 of determining the mass flow through the compressor. Astep 306 is thereafter performed in which a compressor speed value iscalculated as a function of the temperature difference across thecompressor and the mass flow. A final step 308 may be performed in whichthe modeled speed value is communicated to a unit, in line what has beenpreviously described for the controller 200. The method may performadditional steps as has been described above.

In FIG. 7 another method 400 for modeling the speed of a compressor of aturbocharger is schematically shown. The method 400 comprises a firststep 402 of determining the ambient pressure, and a second step 404 ofdetermining if the ambient pressure is below a preset ambient pressurecorresponding to high altitude conditions. If so, the method 400 setsthe ambient pressure as the preset ambient pressure. A third step 406 isperformed for determining a pressure ratio from the boost pressure andthe ambient pressure. In step 408, a compressor speed value is estimatedusing the pressure ratio as input, and

In step 410 a corrected compressor speed value is calculated from theestimated compressor speed value and the actual ambient pressure.Additional steps may be performed, e.g. in which the modeled speed valueis communicated to a unit, in line what has been previously describedfor the controller 200. The method may perform additional steps as hasbeen described above.

The methods 300, 400 of FIGS. 6 and 7 may preferably be combined inorder to provide an improved compressor speed model, especially in termsof simplicity and accuracy.

It is to be understood that the present invention is not limited to theembodiments described above and illustrated in the drawings; rather, theskilled person will recognize that many changes and modifications may bemade within the scope of the appended claims.

The invention claimed is:
 1. A method for modeling the compressor speedof a turbocharger, comprising: determining the temperature differenceacross the compressor, determining the mass flow through the compressor,and calculating a compressor speed value as a function of thetemperature difference across the compressor and the mass flow, whereinthe step of calculating the compressor speed value is performed using${N_{turbo} \propto {\frac{{dm}_{gas}}{dt}{\overset{\sim}{R}\left( {T_{boost} - T_{in}} \right)}}},$where N_(turbo) is the compressor speed, $\frac{{dm}_{gas}}{dt}$ is themass flow, {tilde over (R)} is a corrected ideal gas constant, andT_(boost)−T_(in) is the temperature difference across the compressor. 2.The method according to claim 1, wherein$N_{turbo} \propto {\frac{{dm}_{gas}}{dt}{\overset{\sim}{R}\left( {T_{boost} - T_{in}} \right)}}$is calculated using$N_{turbo} = {{F\left( {\frac{{dm}_{gas}}{dt},{T_{boost} - T_{in}}} \right)}.}$3. The method according to claim 2, wherein the step of calculating thecompressor speed value is performed by a polynomial representation of$N_{turbo} = {F\left( {\frac{{dm}_{gas}}{dt},{T_{boost} - T_{in}}} \right)}$according to:${F\left( {\frac{{dm}_{gas}}{dt},{T_{boost} - T_{in}}} \right)} = {{F\left( {x,y} \right)} = {{a_{1}x^{2}} + {a_{2}{xy}} + {a_{3}y^{2}} + {a_{4}x} + {a_{5}y} + {a_{6}.}}}$4. The method according to claim 1, comprising: determining if arecovered exhaust gas flow is introduced downstream the compressor, andwherein the step of determining the mass flow is performed bydetermining the mass flow of the gas exiting the compressor andcorrecting the determined mass flow by a factor corresponding torecovered exhaust gas flow.
 5. The method according to claim 1, whereinthe step of determining the temperature difference across the compressoris performed by estimating the temperature downstream the compressor,and by subtracting the estimated temperature from a measured ambienttemperature.
 6. The method according to claim 5, wherein the step ofestimating the temperature downstream the compressor is performed bymeasuring the temperature in an air inlet manifold, and correcting thistemperature by a factor corresponding to the temperature loss across anassociated cooler.
 7. The method according to claim 1, comprising:determining the pressure ratio across the compressor, and wherein thestep of calculating the compressor speed value is performed bycalculating the compressor speed value as a function of the pressureratio.
 8. The method according to claim 7, wherein the step ofdetermining the pressure ratio across the compressor is performed by:determining if the ambient pressure is below a preset ambient pressurecorresponding to high altitude conditions, and if so, setting theambient pressure as the preset ambient pressure, and dividing the boostpressure with the ambient pressure.
 9. The method according to claim 8,wherein the step of calculating the compressor speed value is performedby estimating a compressor speed value using the pressure ratio asinput, and calculating a corrected compressor speed value from theestimated compressor speed value and the actual ambient pressure.
 10. Acomputer comprising a computer program for performing the steps of claim1 when the program is run on the computer.
 11. A non-transitory computerreadable medium carrying a computer program for performing the steps ofclaim 1 when the program product is run on a computer.
 12. A controllerfor modeling the compressor speed of a turbocharger, the controllerbeing configured to perform the steps of the method according toclaim
 1. 13. A vehicle comprising a controller according to claim 12.